Bathrrom Tile, Plaster

The tile around the bathtub have begin to loosen and fall off. Iíve removed several rows where the knobs and faucet are and found that the plaster is breaking away from the lath. I had planned on removing and replacing all of tile. I purchased backer board hoping I would be able to screw them on to the studs for retiling. Iíve found that my bathroom does not have stubs, the walls are plaster. (old apt. building) Is there anyway to attached the backer board or will I have to re-plaster the entire bathroom (5 X 7) if so is this a DIY job, or should I spend to have a contractor do the job.